No. You have differentiated the outer process, being the "raised to the sixth power". You now need to differentiate the inner process, being the polynomial. In other words, you need to apply the Chain Rule to complete this differentiation.

mike09 wrote:whereas if the problem were f(x)=3x(x^5 +x)^6 you would have to use the product rule followed by the chain rule correct?

No. You have differentiated the outer process, being the "raised to the sixth power". You now need to differentiate the inner process, being the polynomial. In other words, you need to apply the Chain Rule to complete this differentiation.

mike09 wrote:whereas if the problem were f(x)=3x(x^5 +x)^6 you would have to use the product rule followed by the chain rule correct?

This would involve both the Product Rule and the Chain Rule, yes.

Thank you so much for helping me out.....now that I applied the chain rule to the polynomial would the answer be 18(x^5 + x)^5(5x^4 + 1)?